The Brownian mean field model

European Physical Journal B

Volumn 87, Issue 5, 2014, Pages

  Chavanis, Pierre Henri ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BIOCHEMISTRY; BOLTZMANN EQUATION; BROWNIAN MOVEMENT; MAGNETIZATION; MEAN FIELD THEORY; STOCHASTIC SYSTEMS; SYNCHRONIZATION; THERMODYNAMICS;

ANALYTICAL EXPRESSIONS; BOLTZMANN DISTRIBUTION; COLLECTIVE SYNCHRONIZATION; CRITICAL TEMPERATURES; HAMILTONIAN MEAN FIELD MODELS; LONG RANGE INTERACTIONS; MEAN FIELD APPROXIMATION; SECOND-ORDER PHASE TRANSITION;

HAMILTONIANS;

EID: 84901826461     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2014-40586-6     Document Type: Article

References (77)

1. Dynamics and thermodynamics of systems with long-range interactions, edited by T. Dauxois et al., Lecture Notes in Physics (Springer, 2002), Vol. 602
2. Dynamics and thermodynamics of systems with long-range interactions: Theory and experiments, edited by A. Campa et al., AIP Conf. Proc. 970 (AIP, 2008), Vol. 970
3. Long-Range Interacting Systems, edited by T. Dauxois, S. Ruffo, L. Cugliandolo, Les Houches Summer School 2008 (Oxford University Press, Oxford, 2009)
4. A. Campa, T. Dauxois, S. Ruffo, Phys. Rep. 480, 57 (2009)
5. J. Binney, S. Tremaine, Galactic Dynamics (Princeton Series in Astrophysics, 1987)
6. P.K. Newton, The N-Vortex Problem: Analytical Techniques, in Applied Mathematical Sciences (Springer-Verlag, Berlin, 2001), Vol. 145
7. P.H. Chavanis, A&A 356, 1089 (2000)
8. P.H. Chavanis, C. Sire, Phys. Rev. E 73, 066103 (2006) (Pubitemid 43837765)
9. E. Keller, L.A. Segel, J. Theor. Biol. 26, 399 (1970)
10. P.H. Chavanis, Physica A 384, 392 (2007) (Pubitemid 47285597)
11. M. Antoni, S. Ruffo, Phys. Rev. E 52, 2361 (1995)
12. V. Latora, A. Rapisarda, C. Tsallis, Phys. Rev. E 64, 056134 (2001)
13. V. Latora, A. Rapisarda, C. Tsallis, Physica A 305, 129 (2002) (Pubitemid 34222973)
14. Y.Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, Physica A 337, 36 (2004)
15. F. Bouchet, T. Dauxois, Phys. Rev. E 72, 045103 (2005) (Pubitemid 43273115)
16. P.H. Chavanis, J. Vatteville, F. Bouchet, Eur. Phys. J. B 46, 61 (2005) (Pubitemid 41144039)
17. H. Morita, K. Kaneko, Phys. Rev. Lett. 96, 050602 (2006) (Pubitemid 43270969)
18. P.H. Chavanis, Eur. Phys. J. B 53, 487 (2006) (Pubitemid 44780709)
19. A. Antoniazzi, D. Fanelli, J. Barré, P.H. Chavanis, T. Dauxois, S. Ruffo, Phys. Rev. E 75, 011112 (2007) (Pubitemid 46134145)
20. A. Antoniazzi, F. Califano, D. Fanelli, S. Ruffo, Phys. Rev. Lett. 98, 150602 (2007) (Pubitemid 46582701)
21. A. Antoniazzi, D. Fanelli, S. Ruffo, Y. Yamaguchi, Phys. Rev. Lett. 99, 040601 (2007) (Pubitemid 47171670)
22. A. Campa, A. Giansanti, G. Morelli, Phys. Rev. E 76, 041117 (2007) (Pubitemid 47569138)
23. P.H. Chavanis, G. De Ninno, D. Fanelli, S. Ruffo, in Chaos, Complexity and Transport, edited by C. Chandre, X. Leoncini, G. Zaslavsky (World Scientific, Singapore, 2008), p. 3
24. A. Campa, P.H. Chavanis, A. Giansanti, G. Morelli, Phys. Rev. E 78, 040102(R) (2008)
25. R. Bachelard, C. Chandre, D. Fanelli, X. Leoncini, S. Ruffo, Phys. Rev. Lett. 101, 260603 (2008)
26. R. Bachelard, C. Chandre, A. Ciani, D. Fanelli, Y.Y. Yamaguchi, Phys. Lett. A 373, 4239 (2009)
27. F. Staniscia, P.H. Chavanis, G. De Ninno, D. Fanelli, Phys. Rev. E 80, 021138 (2009)
28. A. Campa, P.H. Chavanis, J. Stat. Mech. 2010, P06001 (2010)
29. P.H. Chavanis, A. Campa, Eur. Phys. J. B 76, 581 (2010)
30. J. Barré, A. Olivetti, Y.Y. Yamaguchi, J. Phys. A 44, 5502 (2011)
31. S. Ogawa, Y. Yamaguchi, Phys. Rev. E 84, 061140 (2011)
32. R. Pakter, Y. Levin, Phys. Rev. Lett. 106, 200603 (2011)
33. T.M. Rocha Filho, M.A. Amato, A. Figueiredo, Phys. Rev. E 85, 062103 (2012)
34. A. Campa, P.H. Chavanis, Eur. Phys. J. B 86, 170 (2013)
35. W. Ettoumi, M.C. Firpo, Phys. Rev. E 87, 03102 (2013)
36. P.H. Chavanis, F. Baldovin, E. Orlandini, Phys. Rev. E 83, 040101(R) (2011)
37. F. Baldovin, P.H. Chavanis, E. Orlandini, Phys. Rev. E 79, 011102 (2009)
38. F. Baldovin, E. Orlandini, Phys. Rev. Lett. 96, 240602 (2006) (Pubitemid 43938687)
39. F. Baldovin, E. Orlandini, Phys. Rev. Lett. 97, 100601 (2006) (Pubitemid 44330973)
40. C. Pichon, Ph.D. thesis, Cambridge (1994)
41. J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chaté, G. Theraulaz, PLoS Comput. Biol. 8, e1002678 (2012)
42. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012)
43. F. Peruani, A. Deutsch, M. Bär, Eur. Phys. J. Special Topics 157, 111 (2008)
44. T. Vicsek, A. Zafeiris, Phys. Rep. 517, 71 (2012)
45. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984)
46. E. Shahmoon, I. Mazets, G. Kurizki, arXiv:1309.0555 (2013)
47. S. Gupta, A. Campa, S. Ruffo, Phys. Rev. E 86, 1130 (2012)
48. J. Heyvaerts, Mon. Not. R. Astron. Soc. 407, 355 (2010)
49. P.H. Chavanis, Physica A 391, 3680 (2012)
50. R.C. Desai, R. Zwanzig, J. Stat. Phys. 19, 1 (1978)
51. D.A. Dawson, J. Stat. Phys. 31, 29 (1983)
52. M. Shiino, Phys. Rev. A 36, 2393 (1987)
53. H. Sakaguchi, Prog. Theor. Phys. 79, 39 (1988)
54. S.H. Strogatz, R.E. Mirollo, J. Stat. Phys. 63, 613 (1991)
55. J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005) (Pubitemid 41490657)
56. P. Reimann, R. Kawai, C. Van den Broeck, P. Hänggi, Europhys. Lett. 43, 545 (1999)
57. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) (Pubitemid 128022013)
58. S. Gupta, A. Campa, S. Ruffo, Phys. Rev. E 89, 022123 (2014)
59. B. Sonnenschein, L. Schimansky-Geier, Phys. Rev. E 88, 052111 (2013)
60. M. Kac, G.E. Uhlenbeck, P.C. Hemmer, J. Math. Phys. 4, 216 (1963)
61. P.H. Chavanis, Physica A 387, 5716 (2008)
62. H. Touchette, Phys. Rep. 478, 1 (2009)
63. H. Risken, The Fokker-Planck equation (Springer, New York, 1989)
64. L. Landau, E. Lifshitz, Fluid Mechanics (Pergamon, London, 1959)
65. P.H. Chavanis, A&A 432, 117 (2005) (Pubitemid 40338898)
66. P.H. Chavanis, L. Delfini, Phys. Rev. E 89, 032139 (2014)
67. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Frontiers in Physics, 1994)
68. D.S. Dean, J. Phys. A 29, L613 (1996)
69. P.H. Chavanis, arXiv:1007.4916 (2010)
70. P.H. Chavanis, L. Delfini, Eur. Phys. J. B 69, 389 (2009)
71. P.H. Chavanis, Eur. Phys. J. B 80, 275 (2011)
72. J. Messer, H. Spohn, J. Stat. Phys. 29, 561 (1982)
73. S. Inagaki, Prog. Theor. Phys. 90, 557 (1993)
74. J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, J. Stat. Phys. 119, 677 (2005) (Pubitemid 40937202)
75. J.J. Monaghan, Mon. Not. R. Astron. Soc. 184, 25 (1978)
76. J. Katz, I. Okamoto, Mon. Not. R. Astron. Soc. 317, 163 (2000)
77. R. Kubo, Rep. Prog. Phys. 29, 255 (1966)